While reading through the new paper in JVP on size estimates in theropods, I
came across several points which I think deserve comment-

The authors find a relationship between skull and body length in theropods
(excluding therizinosaurs, oviraptorosaurs and ornithomimosaurs), then test
it using Sinraptor dongi, Velociraptor, Carnotaurus, NGMC 91 and Mei (none
of which were used to model the relationship originally). They find-

"The body length estimates for Sinraptor and Velociraptor are extremely
close to the published length for the specimens considered (<3.3%), which
reinforce the validity of SK-BL."

And yet the published length of Sinraptor dongi is just another estimate,
since only a few proximal caudals were preserved. Same for Velociraptor, as
the specimen used (AMNH 6515) is just a skull and phalanges.

"Interestingly, the body length of Mei long and of the small feathered NGMC
91 is overestimated (36% and 85%, respectively) by the SK-BL regression
whereas that of Carnotaurus is underestimated (28%). These latter results
reflect the facts that juvenile theropods have larger heads relative to
their body size than adults (Ji et al., 2001; Xu and Norell, 2004) and that
abelisaurids have shorter heads relative to their body size than other
theropods (Bonaparte et al. 1990). Consequently, the SK-BL regression should
not be used for abelisaurids or juvenile individuals."

Er, maybe it's because Mei and NGMC 91 both have much shorter tails (3.17
and 3.6 times femoral length respectively) than any other theropods used,
especially small ones.

Indeed, their figure 2 shows sillouettes of Compsognathus, Coelophysis,
Allosaurus and Tyrannosaurus scaled to a standard total length to illustrate
how relative skull length supposedly increases with increased total length.
What should be obvious from the picture is that this is due to the
increasingly shorter tails of the taxa! Compsognathus' tail is >6.4 times
its femoral length, Allosaurus' is ~5.1, and Tyrannosaurus' is ~4.6.

The dataset shows a bias for short-tailed larger theropods (7 tyrannosaurids
vs. 3 carnosaurs, Dilophosaurus and Ceratosaurus) and long-tailed smaller
theropods (2 coelophysids, 3 compsognathids and Deinonychus vs. 1
troodontid). Note also that tyrannosaurs (especially the larger
tyrannosaurines, especially the largest Tyrannosaurus) are known to be
comparatively more heavily built than other theropods. Examining the
dataset, their Allosaurus fragilis specimen is not YPM 1930 (the fragmentary
holotype), but is USNM 4734 (the topotype). I really don't see why
Carnotaurus, Huaxiagnathus, Juravenator, Mei, NGMC 91 and Sinraptor
hepingensis are included in the "incomplete" dataset. They're more complete
than Acrocanthosaurus, Deinonychus, and the Compsognathus holotype, which
are all in the "complete" dataset. Indeed, the Deinonychus specimen is just
a partial skull.

The authors go on to estimate the length and mass of Spinosaurus, based on
the new large snout (MSNM V4047) described by Del Sasso et al. (2005). They
say-

"A note of caution concerns the dimension of the reconstructed Spinosaurus
skull. First, the proposed skull restoration (Dal Sasso et al. 2005:fig. 5B)
is a composite reconstruction with the front and back halves being from
different genera. Because skull shape varies among spinosaurids (i.e., the
shape of the rostrum, the relative dimensions of the maxillae and
premaxillae, and the shape of posterior region of the skull differ among
spinosaurids; Fig. 3), there is potential for overestimating the length of a
composite spinosaur skull."

Figure 3 shows the skulls of Baryonyx, Suchomimus and Irritator, with known
parts outlined darkly. Yet not only is the old reconstruction of Baryonyx
used (from Charig and Milner, 1997), but the authors failed to realize the
reconstruction of Suchomimus (from Sereno et al., 1998) is mostly based on
Baryonyx (except the premaxilla and maxilla)! Furthermore, reconstructing
Spinosaurus based on the elongate baryonychine morphology instead of
Irritator would result in a longer skull length if anything.

First, the authors test their skull vs. length and skull vs. mass
relationships with more complete spinosaurids. They get results close to
previous estimates, claiming this proves the method works for spinosaurids.
Yet Suchomimus' skull is only known from the snout, while the proximal snout
of Baryonyx is missing. Even worse, the incomplete skeleton of Suchomimus
is headless! The snout and other cranial elements (quadrates and dentaries)
are referred specimens with unknown scaling relative to the postcrania! So
we don't know the skull length of either taxon or the skeletal length
relative to skull length in Suchomimus, making it impossible to confirm
their method works on spinosaurids.

Then they estimate Spinosaurus' length and mass based on their equations and
Dal Sasso et al.'s 1.75 meter skull length estimate. They get a much
shorter (14.34 m) and heavier (20.9 tons) animal than Dal Sasso et al. did.
Why? I'd say because of what I wrote above regarding their biased sample of
large theropods. The large theropods are mostly short-tailed and massive
tyrannosaurids, and the largest are especially massive tyrannosaurines.
Spinosaurus probably had a much longer tail than tyrannosaurids and was more
lightly built, yet because it's skull is longer than any theropod used in
the model, it will be forced into the trendline formed by the largest
tyrannosaurids.

Yet it gets worse, as the authors carpriciously revise Spinosaurus' skull
length to 1.5 meters, resulting in a total length of 12.57 meters, "a value
very close to the body length of the largest theropods known (e.g.,
Tyrannosaurus, Carcharodontosaurus, Giganotosaurus)." "Consequently, the
body length and body mass estimates for this individual are subject to
change and could be considerably lower?possibly 12.57 m and 12 tons?within
the range of the largest theropods known." The Spinosaurus skull
reconstruction is rather crammed posteriorly as it is, with the
laterotemporal fenestra extending below the orbit and such. I don't see how
you could make a realistic reconstruction 1.5 meters long. Look at figure 4
in Dal Sasso et al. (2005) and see if you think MSNM V4047 was only 22%
larger than Suchomimus.

"It is generally accepted that large hadrosaurs, including those smaller
than the 17-m-long Shantungosaurus, were primarily quadrupedal
(Brett-Surman, 1997; Dilkes, 2001), which suggests
that bipedalism at extremely large body size is impractical. In light of the
results presented above, we conclude that it is doubtful that a bipedal
theropod with a mass exceeding 20 tons could have existed. Although it was a
large theropod, Spinosaurus aegyptiacus was probably no larger than the
currently known largest tyrannosaurids and carcharodontosaurids, a size
close to the biomechanical limit for strictly bipedal animals (Henderson,
2005)."

Or maybe it suggests that spinosaurids weren't hadrosaurs. Hadrosaurs of
any size were primarily quadrupedal. It's just as meaningless as showing
large sauropods were quadrupedal.

In conclusion, while it would be nice to have a formula to estimate theropod
length and weight with based on skull size, I believe it's wishful thinking.
Therrien and Handerson show you can get decent results if you limit taxon
selection, but it's much better to use related taxa and scale to known
proportions. Even better, find allometric relationships within known taxa
(e.g. tyrannosaurids).